Such seal segment assemblies having honeycomb-structured sealing members are known. The honeycomb-structured sealing members are typically brazed onto the carrier base. The seal carrier is negligibly stiff, in particular circumferentially. This is hardly enhanced by the honeycomb-structured sealing member since the honeycomb cells themselves are not particularly stiff, even circumferentially. Since it is desired that the seal carrier including the sealing member be as flat as possible in the radial direction, the entire component is negligibly stiff.